In a certain lottery drawing, five balls are selected from a tumbler in which each ball is printed with a different two-digit positive integer. if the average (arithmetic mean) of the five numbers drawn is 56 and the median is 60, what is the greatest value that the lowest number selected could be?

48

Since the mean is 56 for 5 balls, that means that the sum of all 5 balls is 5*56 = 280. And since the median is 60, that means that 2 balls have values less than 60 and 2 have values greater than 60, and the sum of the 4 unknown balls is 280-60 = 220. Now since we want to know the greatest value of the lowest ball selected, we need to "save up" as much of the 220 value as possible. So let's choose the smallest possible values for the 2 balls with a value greater than the median, those values would be 61 and 62. So we now have 220-61-62 = 97 as the largest possible sum of the 2 balls less than 60. And since we're looking for the greatest possible value of the lowest scoring ball, let's call that X and the next higher ball would be X+1. So we have X + X + 1 = 97, 2X + 1 = 97, 2X = 96, X = 48. So the greatest possible value of the lowest number selected is 48.